A projectile launched from the ground with an initial speed of 20 m/s and a launch angle u follows a trajectory approximated by

x = (20 cos θ)t, y = -4.9t² + (20 sin θ)t,

where x and y are the horizontal and vertical positions of the projectile relative to the launch point (0, 0).

a. Graph the trajectory for various values of u in the range 0 < θ < π/2.

b. Based on your observations, what value of θ gives the greatest range (the horizontal distance between the launch and landing points)?